I would like to (randomly?) amplify the stuff in post 665.
More effort is spent in reducting randomness or uncertainty than in amplifying it. (In general only for simulation or cryptography or sampling, etc. does one want more uncertainty.)
One obvious method to reduce uncertainty is to measure with more precise instruments.
A less obvious method (which can sometimes be used when the previous idea fails) is to average values. Under some technical conditions (finite variance or satisfyint the Lindeberg-Feller conditions, for example), an average is a better estimate of the "center" of a distribution of values than is any individual value. Bigger samples also yield smaller uncertainties which is why political pollsters try for big samples.
Good example: in a sample from a normal distribution (a "bell curve" for those with degrees in Education); the sample average is a better estimate for the center than any individual.
Borderline counterexample: in a sample from a Cauchy distribution (the distribution of brightness from a flashlight that shines on an wall), the sample average is no better than any single sample as an estimate of the center. This is a strange distribution with undefined mean and infinite variance.
Really ugly counterexample: take a sample from a normal distribution and for each item take its reciprocal. The sample average is much worse than any single sample value as an estimate of the center.
The point is, the "rules and procedures" for working with uncertainty are not always obvious or simple. Intuition must be developed. Trick question: what is the probability of gettin HH in a series of coin throws before getting TH?
Very interesting. I wonder if any dialogue can bring DS's last into the vicinity of yours. If I follow the outline, his enumerations suggests that naive experience is not sufficent for the determination of life non-life, that (according to one poster) we really ought to put such fallacious determinations out of the reach of science, but that perhaps intuition and precision of tools might still raise the certainty wherein lies the truth (according to another poster).
And, what consequence follows from accepting this big gap between certainty and naive experience. And, who has set for us the bar for certainty?
25%